Meanwhile, they have more jobs to choose from. Employers expect to hire 10.2% more graduates this year than they did last year, according to NACE's survey of 160 employers.

These employers have posted 15,767 job openings for college graduates this year -- up about 10% from the 14,341 that were posted for the Class of 2011 and more than triple the mere 5,174 job postings for the Class of 2010.

But the competition is steep, with employers reporting that they have received nearly 33 applications for every job posting, up from 21 applications per posting last year.

The major in highest demand is engineering, with 69% of employers in that field saying they are hiring graduates. Business majors are next on the list, with 63% of employers hiring. Accounting, Computer Science and Economics are also among the top five most-desired majors.

These are also the fields with the highest-paying jobs, according to a separate survey NACE conducted this year. Employers in each of these areas are paying median salaries above $40,000 to this year's graduates.

Engineering jobs pay the most -- with this year's graduates starting at a median salary of $58,581, which is relatively unchanged from last year.

But even some of the jobs that don't typically pay as well posted increases in salaries this year. Education-related salaries increased 4.5% to a median $37,423, while salaries in the communications field rose nearly 4% to $40,022.